Dueling deep neural networks

ABSTRACT

Systems, methods, and apparatus, including computer programs encoded on a computer storage medium, for selecting an actions from a set of actions to be performed by an agent interacting with an environment. In one aspect, the system includes a dueling deep neural network. The dueling deep neural network includes a value subnetwork, an advantage subnetwork, and a combining layer. The value subnetwork processes a representation of an observation to generate a value estimate. The advantage subnetwork processes the representation of the observation to generate an advantage estimate for each action in the set of actions. The combining layer combines the value estimate and the respective advantage estimate for each action to generate a respective Q value for the action. The system selects an action to be performed by the agent in response to the observation using the respective Q values for the actions in the set of actions.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. application Ser. No. 15/349,900, filed onNov. 11, 2016, which claims priority to U.S. Provisional Application No.62/254,684, filed on Nov. 12, 2015. The disclosures of the priorapplications are considered part of and are incorporated by reference inthe disclosure of this application.

BACKGROUND

This specification relates to reinforcement learning.

In a reinforcement learning system, an agent interacts with anenvironment by performing actions that are selected by the reinforcementlearning system in response to receiving observations that characterizethe current state of the environment.

Some reinforcement learning systems select the action to be performed bythe agent in response to receiving a given observation in accordancewith an output of a neural network.

Neural networks are machine learning models that employ one or morelayers of nonlinear units to predict an output for a received input.Some neural networks are deep neural networks that include one or morehidden layers in addition to an output layer. The output of each hiddenlayer is used as input to the next layer in the network, i.e., the nexthidden layer or the output layer. Each layer of the network generates anoutput from a received input in accordance with current values of arespective set of parameters.

SUMMARY

In general, one innovative aspect of the subject matter described inthis specification can be embodied in systems for selecting actions froma set of actions to be performed by an agent interacting with anenvironment, where the systems include a dueling deep neural networkimplemented by one or more computers.

The dueling deep neural network includes: (i) a value subnetworkconfigured to receive a representation of an observation characterizinga current state of the environment and process the representation of theobservation to generate a value estimate, the value estimate being anestimate of an expected return resulting from the environment being inthe current state; (ii) an advantage subnetwork configured to receivethe representation of the observation and process the representation ofthe observation to generate a respective advantage estimate for eachaction in the set of actions that is an estimate of a relative measureof the return resulting from the agent performing the action when theenvironment is in the current state relative to the return resultingfrom the agent performing other actions when the environment is in thecurrent state; and (iii) a combining layer configured to, for eachaction, combine the value estimate and the respective advantage estimatefor the action to generate a respective Q value for the action, whereinthe respective Q value is an estimate of an expected return resultingfrom the agent performing the action when the environment is in thecurrent state.

Other embodiments of this aspect include methods for using the systemsto select actions to be performed by an agent interacting with anenvironment. Other embodiments of this aspect include correspondingcomputer systems, apparatus, and computer programs recorded on one ormore computer storage devices, each configured to perform the actions ofthe methods. A system of one or more computers can be configured toperform particular operations or actions by virtue of software,firmware, hardware, or any combination thereof installed on the systemthat in operation may cause the system to perform the actions. One ormore computer programs can be configured to perform particularoperations or actions by virtue of including instructions that, whenexecuted by data processing apparatus, cause the apparatus to performthe actions.

In some implementations, the system comprises one or more secondcomputers and one or more storage devices storing instructions that whenexecuted by the one or second more computers cause the one or moresecond computers to perform operations including selecting an action tobe performed by the agent in response to the observation using therespective Q values for the actions in the set of actions.

In some implementations, the dueling deep neural network furtherincludes one or more initial neural network layers configured to receivethe observation and process the observation to generate therepresentation of the observation.

In some implementations, the observation is an image and the one or moreinitial neural network layers are convolutional neural network layers.In some implementations, the representation of the observation is theobservation.

In some implementations, combining the value estimate and the respectiveadvantage estimate includes determining a measure of central tendency ofthe respective advantage estimates for the actions in the set ofactions; determining a respective adjusted advantage estimate for theaction by adjusting the respective advantage estimate for the actionusing the measure of central tendency; and combining the respectiveadvantage estimate for the action and the value estimate to determinethe respective Q value for the action.

In some implementations, the value subnetwork has a first set ofparameters and the advantage subnetwork has a second, different set ofparameters.

In some implementations, selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions includes selecting an action having ahighest Q value as the action to be performed by the agent.

In some implementations, selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions includes selecting a random actionfrom the set of actions with probability ε and selecting an actionhaving a highest Q value with probability 1−ε.

Another innovative aspect of the subject matter disclosed in thisspecification can be embodied in methods for selecting actions from aset of actions to be performed by an agent interacting with anenvironment using a dueling deep neural network comprising a valuesubnetwork and an advantage subnetwork, where the methods includes theactions of obtaining a representation of an observation characterizing acurrent state of the environment; processing the representation of theobservation using the value subnetwork, wherein the value subnetwork isconfigured to receive the representation of the observation and processthe representation of the observation to generate a value estimate, thevalue estimate being an estimate of an expected return resulting fromthe environment being in the current state; processing therepresentation of the observation using the advantage subnetwork,wherein the advantage subnetwork is configured to receive therepresentation of the observation and process the representation of theobservation to generate a respective advantage estimate for each actionin the set of actions that is an estimate of a relative measure of thereturn resulting from the agent performing the action when theenvironment is in the current state relative to the return resultingfrom the agent performing other actions when the environment is in thecurrent state; for each action, combining the value estimate and therespective advantage estimate for the action to generate a respective Qvalue for the action, wherein the respective Q value is an estimate ofan expected return resulting from the agent performing the action whenthe environment is in the current state; and selecting an action to beperformed by the agent in response to the observation using therespective Q values for the actions in the set of actions.

Other embodiments of this aspect include corresponding computer systems,apparatus, and computer programs recorded on one or more computerstorage devices, each configured to perform the actions of the methods.A system of one or more computers can be configured to performparticular operations or actions by virtue of software, firmware,hardware, or any combination thereof installed on the system that inoperation may cause the system to perform the actions. One or morecomputer programs can be configured to perform particular operations oractions by virtue of including instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the actions. Insome implementations, the dueling deep neural network further includesone or more initial neural network layers, and the methods furtherinclude processing the observation using the one or more initial neuralnetwork layers, wherein the one or more initial neural network layersare configured to receive the observation and process the observation togenerate the representation of the observation.

In some implementations, the observation is an image and wherein the oneor more initial neural network layers are convolutional neural networklayers. In some implementations, the representation of the observationis the observation.

In some implementations, combining the value estimate and the respectiveadvantage estimate includes: determining a measure of central tendencyof the respective advantage estimates for the actions in the set ofactions; determining a respective adjusted advantage estimate for theaction by adjusting the respective advantage estimate for the actionusing the measure of central tendency; and combining the respectiveadvantage estimate for the action and the value estimate to determinethe respective Q value for the action.

In some implementations, the value subnetwork has a first set ofparameters and the advantage subnetwork has a second, different set ofparameters.

In some implementations, selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions includes selecting an action having ahighest Q value as the action to be performed by the agent.

In some implementations, selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions includes selecting a random actionfrom the set of actions with probability ε and selecting an actionhaving a highest Q value with probability 1−ε.

The subject matter described in this specification can be implemented inparticular embodiments so as to realize one or more of the followingadvantages. Neural networks can be trained to generate better advantageestimates. Training a neural network to generate reliable advantageestimates can be computationally more complex than training a neuralnetwork to generate reliable value estimates. This is because advantageestimates have to take into account the properties both of the state ofan agent's environment and the advantage of each individual action inthat state, while value estimates are based on properties of theenvironment state alone. Allocating a separate subnetwork for generatingadvantage estimates enables generalized training of neural networks forgenerating advantage estimates across different actions without the needto change the underlying reinforcement learning algorithm. This leads tothe generation of advantage estimates and Q values that are moreaccurate and mitigates or overcomes the difficulties in generatingreliable advantage estimates detailed above. The improved accuracy ofgenerated Q values can be especially significant in cases in which thetarget values for advantage estimates and Q values of different actionsare close to each other.

The details of one or more embodiments of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example reinforcement learning system.

FIG. 2 is a flow chart of an example process for selecting an action tobe performed by an agent.

FIG. 3 is a flow chart of an example process for generating Q valuesusing adjusted advantage estimates.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This specification generally describes a reinforcement learning systemthat selects actions to be performed by a reinforcement learning agentinteracting with an environment. In order for the agent to interact withthe environment, the system receives data characterizing the currentstate of the environment and selects an action from a predetermined setof actions to be performed by the agent in response to the receiveddata. Data characterizing a state of the environment will be referred toin this specification as an observation.

In some implementations, the environment is a simulated environment andthe agent is implemented as one or more computer programs interactingwith the simulated environment. For example, the simulated environmentmay be a video game and the agent may be a simulated user playing thevideo game. As another example, the simulated environment may be amotion simulation environment, e.g., a driving simulation or a flightsimulation, and the agent is a simulated vehicle navigating through themotion simulation. In these implementations, the actions may be controlinputs to control the simulated user or simulated vehicle.

In some other implementations, the environment is a real-worldenvironment and the agent is a mechanical agent interacting with thereal-world environment. For example, the agent may be a robotinteracting with the environment to accomplish a specific task. Asanother example, the agent may be an autonomous or semi-autonomousvehicle navigating through the environment. In these implementations,the actions may be control inputs to control the robot or the autonomousvehicle.

For instance, the agent may be a robotic agent interacting with anenvironment. Observations about this environment may include sensorydata (including images) captured by one or more sensors of the roboticagent and characterizing one or more properties of the environment. Forexample, each observation may include an image captured by a camera ofthe robotic agent and, optionally, one or more other sensor readingscaptured by one or more other sensors of the robotic agent (such asthermal sensors, chemical sensors, motion sensors, etc.).

FIG. 1 shows an example reinforcement learning system 100. Thereinforcement learning system 100 selects actions to be performed by areinforcement learning agent 102 interacting with an environment 104.That is, the reinforcement learning system 100 receives observations,with each observation characterizing a respective state of theenvironment 104, and, in response to each observation, selects an actionfrom a predetermined set of actions to be performed by the reinforcementlearning agent 102 in response to the observation. In response to someor all of the actions performed by the agent 102, the reinforcementlearning system 100 receives a reward. Each reward is a numeric valuereceived from the environment 104 as a consequence of the agentperforming an action, i.e., the reward will be different depending onthe state that the environment 104 transitions into as a result of theagent 102 performing the action.

In particular, the reinforcement learning system 100 selects actions tobe performed by the agent 102 using a dueling deep neural network 103.The dueling deep neural network 103 is a neural network that receives asan input an observation 105 that characterizes the current state of theenvironment 104 and generates a respective Q value 171 for each actionin the set of actions.

The Q value for a given action is an estimate of the expected returnresulting from the agent 102 performing the given action in response tothe observation 105. The return is a measure of the total long-termfuture reward received by the reinforcement learning system 100 as aresult of the agent performing the action in response to the observation105. For example, the return may be a time-discounted sum of futurerewards.

The dueling deep neural network 103 includes a value subnetwork 111, anadvantage subnetwork 112, and a combining layer 113. The dueling deepneural network 103 may also optionally include initial neural networklayers 110.

When included in the dueling deep neural network 103, the initial neuralnetwork layers 110 are configured to receive the observation 105 and toprocess the observation 105 to generate a representation 151 of theobservation 105. For example, in implementations when the observation isan image, the one or more initial neural network layers 110 may beconvolutional neural network layers that extract features from theimage.

The value subnetwork 111 is configured to process the representation 151or, in implementations where the dueling deep neural network 103 doesnot include any initial neural network layers 100, the observation 105to determine a value estimate 152 for the current state of theenvironment 104. The value estimate 152 for the current state is anestimate of the expected return resulting from the environment being inthe current state. In other words, the value estimate 152 measures theimportance of being in the current state irrespective of the actionselected when the environment 104 is in the current state.

The advantage subnetwork 112 is configured to process the representation151 or, in implementations where the dueling deep neural network 103does not include any initial neural network layers 100, the observation105 to determine a respective advantage estimate 153 for each action inthe set of actions. The advantage estimate 153 for a given action is anestimate of the relative measure of the return resulting from the agentperforming the given action relative to other actions in the set ofactions 106 when the environment 104 is in the current state.

The combining layer 113 is configured to, for each action in the set ofactions, combine the value estimate 152 and the advantage estimate 153for the action to determine a respective Q value 171 for the action.Combining the value estimate 152 and advantage estimate 153 for eachaction is described in greater detail below with reference to FIG. 3.

The reinforcement learning system 100 may optionally include a decisionmaking engine 120. The decision making engine 120 uses the Q values 171for the actions in the set of possible actions 106 to select an actionto be performed by the agent 102 in response to the observation 105 andcauses the agent 102 to perform the selected action.

The dueling deep neural network 103 is implemented by one or more firstcomputers, while the operations for the decision making engine 120 areperformed by one or more second computers.

In some implementations, the one or more first computers may be part ofthe same computer system as the one or more second computers. In otherimplementations, the one or more first computers and the one or moresecond computers may be part of different computer systems.

In some implementations, the one or more first computers and the one ormore second computers consist of the same one or more computers. Inother words, the same one or more computers implement the dueling deepneural network 103 and perform the operations for the decision makingengine 120.

In some implementations, the one or more first computers and the one ormore second computers consist of different one or more computers. Inother words, different one or more computers implement the dueling deepneural network 103 and perform the operations for the decision makingengine 120.

FIG. 2 is a flow chart of an example process 200 for selecting an actionto be performed by an agent. For convenience, the process 200 will bedescribed as being performed by a system of one or more computerslocated in one or more locations. For example, a reinforcing learningsystem, e.g., the reinforcing learning system 100 of FIG. 1,appropriately programmed in accordance with this specification, canperform the process 200.

The system obtains an observation characterizing the current state ofthe environment (210). In some implementations, the observation is animage or a collection of images. For example, the observation may beobtained using one or more sensors associated with the environment orwith the agent.

The system generates a representation of the observation (220). In someimplementations, the representation of the observation is theobservation itself. In some other implementations, the system generatesthe representation of the observation by processing the observationthrough one or more initial neural network layers of a dueling deepneural network (e.g., the initial neural network layers 110 of thedueling deep neural network 103 in FIG. 1).

The system generates a value estimate by processing the representationof the observation (230 using a value subnetwork of a dueling deepneural network (e.g., the value subnetwork 111 of the dueling deepneural network 103 in FIG. 1). The value estimate is an estimate of anexpected return resulting from the environment of the agent being in thecurrent state. In some implementations, the value estimate of aparticular state is the expected return when starting in the particularstate and following a particular policy thereafter, i.e., an actionselection policy defined by the Q values output by dueling deep network.

The system generates an advantage estimate for each action in thepossible set of actions by processing the representation of theobservation (240) using an advantage subnetwork of a dueling deep neuralnetwork (e.g., the advantage subnetwork 112 of the dueling deep neuralnetwork 103 in FIG. 1). The advantage estimate for a given action is anestimate of the relative measure of the return resulting from the agentperforming the action relative to other actions in the set of actionswhen the environment is in a current state.

The system generates Q values for each action by combining a measure ofthe value estimate and a measure of the advantage estimate of the action(250). In some implementations, the system adds the value estimate andthe advantage estimate of an action to generate the Q value of anaction. In some other implementations, the system adds the valueestimate and an adjusted value of the advantage estimate to generate theQ value of an action.

Generating Q values using adjusted advantage estimates is described ingreater detail below with reference to FIG. 3.

The system selects an action to be performed by the agent in response tothe observation (260).

In some implementations, the system selects an action having a highest Qvalue as the action to be performed by the agent. In some otherimplementations, e.g., during the training of the dueling deep neuralnetwork, the system selects a random action from the set of possibleactions with probability ε and selects an action with the highest Qvalue with probability 1−ε. In some of these implementations, the valueof c may decrease as the system is presented with more trainingexamples, which leads to reduced random action selection by the system.

In some implementations, after the dueling deep neural network has beentrained, the system selects the action to be performed using theadvantage estimate of each action, i.e., by selecting the action thathas the highest advantage estimate.

FIG. 3 is a flow chart of an example process 300 for generating Q valuesusing adjusted advantage estimates. For convenience, the process 300will be described as being performed by a system of one or morecomputers located in one or more locations. For example, a reinforcinglearning system, e.g., the reinforcing learning system 100 of FIG. 1,appropriately programmed in accordance with this specification, canperform the process 300.

The system obtains a value estimate for the current state (310).

The system obtains a respective advantage estimate for each action inthe set of possible actions (320).

The system determines a statistic characterizing the advantage estimates(330). In some implementations, the statistic is a measure of centraltendency, e.g., the mean or median of the respective advantageestimates. In some other implementations, the statistic is the maximumof the advantage estimates.

The system determines an adjusted advantage estimate using the statistic(340). In some implementations, the system subtracts the statistic fromthe advantage estimate for each action to determine the adjustedadvantage estimate for the action.

The system generates Q values for each action using the value estimateand the respective advantage estimate (350). That is, the systemcombines the value estimate for the current state and the adjustedadvantage estimate for each action to generate the Q value for eachaction.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non transitory program carrier for execution by, or to controlthe operation of, data processing apparatus. Alternatively or inaddition, the program instructions can be encoded on an artificiallygenerated propagated signal, e.g., a machine-generated electrical,optical, or electromagnetic signal, that is generated to encodeinformation for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them. The computer storage medium is not, however, apropagated signal.

The term “data processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, or multiple processors or computers.The apparatus can include special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application specificintegrated circuit). The apparatus can also include, in addition tohardware, code that creates an execution environment for the computerprogram in question, e.g., code that constitutes processor firmware, aprotocol stack, a database management system, an operating system, or acombination of one or more of them.

A computer program (which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code) can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, e.g., one ormore scripts stored in a markup language document, in a single filededicated to the program in question, or in multiple coordinated files,e.g., files that store one or more modules, sub programs, or portions ofcode. A computer program can be deployed to be executed on one computeror on multiple computers that are located at one site or distributedacross multiple sites and interconnected by a communication network.

As used in this specification, an “engine,” or “software engine,” refersto a software implemented input/output system that provides an outputthat is different from the input. An engine can be an encoded block offunctionality, such as a library, a platform, a software development kit(“SDK”), or an object. Each engine can be implemented on any appropriatetype of computing device, e.g., servers, mobile phones, tabletcomputers, notebook computers, music players, e-book readers, laptop ordesktop computers, PDAs, smart phones, or other stationary or portabledevices, that includes one or more processors and computer readablemedia. Additionally, two or more of the engines may be implemented onthe same computing device, or on different computing devices.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Computers suitable for the execution of a computer program include, byway of example, can be based on general or special purposemicroprocessors or both, or any other kind of central processing unit.Generally, a central processing unit will receive instructions and datafrom a read only memory or a random access memory or both. The essentialelements of a computer are a central processing unit for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer readable media suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto optical disks;

and CD ROM and DVD-ROM disks. The processor and the memory can besupplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's client device in response to requests received from the webbrowser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back end, middleware, or front end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or of what may be claimed, but rather as descriptions offeatures that may be specific to particular embodiments of particularinventions. Certain features that are described in this specification inthe context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various system modulesand components in the embodiments described above should not beunderstood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain implementations, multitasking and parallelprocessing may be advantageous.

What is claimed is:
 1. A system for selecting actions from a set ofactions to be performed by an agent interacting with an environment, thesystem comprising: a dueling deep neural network implemented by one ormore computers, the dueling deep neural network comprising: a valuesubnetwork configured to: receive a representation of an observationcharacterizing a current state of the environment; and process therepresentation of the observation to generate a value estimate, thevalue estimate being an estimate of an expected return resulting fromthe environment being in the current state; an advantage subnetworkconfigured to: receive the representation of the observation; andprocess the representation of the observation to generate a respectiveadvantage estimate for each action in the set of actions that is anestimate of a relative measure of the return resulting from the agentperforming the action when the environment is in the current staterelative to the return resulting from the agent performing other actionswhen the environment is in the current state; and a combining layerconfigured to, for each action, combine the value estimate and therespective advantage estimate for the action to generate a respective Qvalue for the action, wherein the respective Q value is an estimate ofan expected return resulting from the agent performing the action whenthe environment is in the current state.
 2. The system of claim 1,wherein the system comprises one or more second computers and one ormore storage devices storing instructions that when executed by the oneor second more computers cause the one or more second computers toperform operations comprising: selecting an action to be performed bythe agent in response to the observation using the respective Q valuesfor the actions in the set of actions.
 3. The system of claim 1, whereinthe dueling deep neural network further comprises: one or more initialneural network layers configured to: receive the observation; andprocess the observation to generate the representation of theobservation.
 4. The system of claim 3, wherein the observation is animage and wherein the one or more initial neural network layers areconvolutional neural network layers.
 5. The system of claim 1, whereinthe representation of the observation is the observation.
 6. The systemof claim 1, wherein combining the value estimate and the respectiveadvantage estimate comprises: determining a measure of central tendencyof the respective advantage estimates for the actions in the set ofactions; determining a respective adjusted advantage estimate for theaction by adjusting the respective advantage estimate for the actionusing the measure of central tendency; and combining the respectiveadvantage estimate for the action and the value estimate to determinethe respective Q value for the action.
 7. The system of claim 1, whereinthe value subnetwork has a first set of parameters and the advantagesubnetwork has a second, different set of parameters.
 8. The system ofclaim 2, wherein selecting an action to be performed by the agent inresponse to the observation using the respective Q values for theactions in the set of actions comprises: selecting an action having ahighest Q value as the action to be performed by the agent.
 9. Thesystem of claim 2, wherein selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions comprises: selecting a random actionfrom the set of actions with probability ε; and selecting an actionhaving a highest Q value with probability 1−ε.
 10. A method forselecting actions from a set of actions to be performed by an agentinteracting with an environment using a dueling deep neural networkcomprising a value subnetwork and an advantage subnetwork, the methodcomprising: obtaining a representation of an observation characterizinga current state of the environment; processing the representation of theobservation using the value subnetwork, wherein the value subnetwork isconfigured to: receive the representation of the observation; andprocess the representation of the observation to generate a valueestimate, the value estimate being an estimate of an expected returnresulting from the environment being in the current state; processingthe representation of the observation using the advantage subnetwork,wherein the advantage subnetwork is configured to: receive therepresentation of the observation; and process the representation of theobservation to generate a respective advantage estimate for each actionin the set of actions that is an estimate of a relative measure of thereturn resulting from the agent performing the action when theenvironment is in the current state relative to the return resultingfrom the agent performing other actions when the environment is in thecurrent state; for each action, combining the value estimate and therespective advantage estimate for the action to generate a respective Qvalue for the action, wherein the respective Q value is an estimate ofan expected return resulting from the agent performing the action whenthe environment is in the current state; and selecting an action to beperformed by the agent in response to the observation using therespective Q values for the actions in the set of actions.
 11. Themethod of claim 10, wherein the dueling deep neural network furthercomprises one or more initial neural network layers, and wherein themethod further comprises: processing the observation using the one ormore initial neural network layers, wherein the one or more initialneural network layers are configured to: receive the observation; andprocess the observation to generate the representation of theobservation.
 12. The method of claim 11, wherein the observation is animage and wherein the one or more initial neural network layers areconvolutional neural network layers.
 13. The method of claim 10, whereinthe representation of the observation is the observation.
 14. The methodof claim 10, wherein combining the value estimate and the respectiveadvantage estimate comprises: determining a measure of central tendencyof the respective advantage estimates for the actions in the set ofactions; determining a respective adjusted advantage estimate for theaction by adjusting the respective advantage estimate for the actionusing the measure of central tendency; and combining the respectiveadvantage estimate for the action and the value estimate to determinethe respective Q value for the action.
 15. The method of claim 10,wherein the value subnetwork has a first set of parameters and theadvantage subnetwork has a second, different set of parameters.
 16. Themethod of claim 10, wherein selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions comprises: selecting an action havinga highest Q value as the action to be performed by the agent.
 17. Themethod of claim 10, wherein selecting an action to be performed by theagent in response to the observation using the respective Q values forthe actions in the set of actions comprises: selecting a random actionfrom the set of actions with probability ε; and selecting an actionhaving a highest Q value with probability 1−ε.
 18. A computer storagemedium encoded with instructions that, when executed by one or morecomputers, cause the one or more computers to perform operations for amethod for selecting actions from a set of actions to be performed by anagent interacting with an environment using a dueling deep neuralnetwork comprising a value subnetwork and an advantage subnetwork, themethod comprising: obtaining a representation of an observationcharacterizing a current state of the environment; processing therepresentation of the observation using the value subnetwork, whereinthe value subnetwork is configured to: receive the representation of theobservation; and process the representation of the observation togenerate a value estimate, the value estimate being an estimate of anexpected return resulting from the environment being in the currentstate; processing the representation of the observation using theadvantage subnetwork, wherein the advantage subnetwork is configured to:receive the representation of the observation; and process therepresentation of the observation to generate a respective advantageestimate for each action in the set of actions that is an estimate of arelative measure of the return resulting from the agent performing theaction when the environment is in the current state relative to thereturn resulting from the agent performing other actions when theenvironment is in the current state; for each action, combining thevalue estimate and the respective advantage estimate for the action togenerate a respective Q value for the action, wherein the respective Qvalue is an estimate of an expected return resulting from the agentperforming the action when the environment is in the current state; andselecting an action to be performed by the agent in response to theobservation using the respective Q values for the actions in the set ofactions.
 19. The computer storage medium of claim 18, the dueling deepneural network further comprises one or more initial neural networklayers, and wherein the method further comprises: processing theobservation using the one or more initial neural network layers, whereinthe one or more initial neural network layers are configured to: receivethe observation; and process the observation to generate therepresentation of the observation.
 20. The computer storage medium ofclaim 18, wherein combining the value estimate and the respectiveadvantage estimate comprises: determining a measure of central tendencyof the respective advantage estimates for the actions in the set ofactions; determining a respective adjusted advantage estimate for theaction by adjusting the respective advantage estimate for the actionusing the measure of central tendency; and combining the respectiveadvantage estimate for the action and the value estimate to determinethe respective Q value for the action.